This invention relates to a thermal mass flow meter of the MEMS variety, in which the flow sensor is constructed by micromachining techniques on a silicon substrate, and employs a central heater flanked by two or more upstream and downstream temperature detectors all placed in direct thermal contact with the flowing fluid, so that the existence of fluid flow in the upstream or downstream direction causes an imbalance in the temperature detectors indicative of the fluid flow rate. The flow sensor is fabricated on the surface of a silicon crystal and then mounted either as part of an inside wall of a flow channel that carries the fluid flow, or on a membrane or bridge structure that spans the flow channel internally.
Such MEMS flow sensors are known to have output that is sensitive to the thermal and mechanical properties of the fluid flowing through the sensor, such as fluid mass density, specific heat, thermal conductivity, viscosity, etc. and also to environmental variables such as fluid inlet temperature and pressure. These dependencies limit the ability of a user to operate the flow sensor with different fluids and fluid mixtures, unless expensive and time consuming empirical calibration of the MEMS flow sensor with each fluid of interest is first performed.
It is therefore desirable and useful to provide a method of automatically correcting the output of a MEMS thermal flow sensor for different fluid compositions by direct measurement of the relevant fluid properties performed within the flow sensor itself. The invention disclosed below teaches a method for accomplishing this fluid composition correction, enabling a thermal flow sensor calibrated once on a known fluid to measure a wide variety of unknown pure fluids and fluid mixtures without further flow calibration, provided only that a time constant and thermal conductivity representative of the unknown fluid or mixture are first measured within the flow sensor at zero flow.
Note that “fluid” as used in this document denotes any material medium that is capable of flowing through a conduit and being heated or cooled, for example gases, liquids, granular materials, suspensions, mixtures, etc. The principles of thermal flow sensing apply to all fluids in this wider sense. Also, use of the more specific terms gas, liquid, mixture, etc. to describe specific implementations below should not be interpreted in a limiting sense but as instances of “fluids” in the broader sense.
Two other kinds of commercially relevant thermal flow meters exist in the prior art. First are the large insertion probe thermal flow meters that typically use a macroscopic inserted probe that measures flow at one point on the cross-sectional area of the pipe, and typically operate in the turbulent flow regime. In these designs the thermal detectors are not in direct contact with the flowing fluid, but reside behind the protective walls of the metal (typically stainless steel) probe that projects inward radially from the pipe wall where it is attached. These meters must be flow calibrated with the user fluid. They are a direct commercial evolutionary development of the hot-wire anemometers, primarily used for fluid flow research, that are too fragile for use in industrial applications. These insertion probe thermal meters are not used for the same applications, or in the laminar flow regime served by the MEMS variety of thermal flow sensors. They will not be further discussed here. However their characteristics and guidelines for their use are summarized in the two international flow standards, one from ISO, and one from ASME, listed in the References section.
Another kind of thermal flow meter known in the art is the capillary tube thermal flow meter, which has external heating and temperature resistive sensing coils wound on the outside of a small capillary tube, the sensing coils not in direct thermal contact with the flowing fluid, but measuring the temperature of the tube wall that is in direct thermal contact with the flowing fluid at the tube wall inside surface. These flow meters also have sensitivity to fluid or gas composition, but their gas composition dependence is much better understood than the gas composition dependence of MEMs thermal flow meters.
The capillary tube thermal mass flow sensors exhibit at low laminar flows a response that is directly proportional to mass flow rate for all fluids, with a slope that is fluid-dependent. At high laminar flow rates, however, their response becomes a non-linear function of mass flow, that has a more complicated dependence on fluid composition and properties. As first suggested by Blackett (P. M. S. Blackett Proc. Roy Soc. 1930, p. 319 ff), in their linear response range to flow, the capillary tube thermal flow meters respond in direct proportion to the heat capacity per unit time flowing through the tube, and are otherwise independent of fluid composition. Therefore, if the fluid heat capacity per unit mass is known, the capillary meter may be calibrated to read mass flow directly without the requirement to know any other fluid properties. For this technology it is also a simple matter to convert a flow rate measured with one fluid to a flow rate measured with a second fluid passing through the same calibrated flow sensor, by multiplying the sensor flow rate reading by a gas or fluid correction factor. The gas correction factor is simply the ratio of the heat capacities of the two known fluids in the flow region where the sensor response is linear with both fluids. Therefore a capillary thermal flow sensor calibrated on fluid A may be used to measure flow of any known fluid B if the readings are multiplied by the constant gas correction factor that connects fluids A and B. Such capillary tube thermal flow meters are unable to measure the flows of arbitrary unknown pure gases or mixtures, where the gas or gas mixture specific heat capacity is variable or unknown, though they will still respond in proportion to the mass flow rate, i.e. for unknown gases of constant composition they behave like a flow meter that is not calibrated. As they have no way to distinguish a changing fluid specific heat from a changing fluid mass flow rate, being sensitive only to the product of the two quantities, the capillary tube thermal sensors cannot be used directly to measure the flow rate of a fluid mixture that has time-varying composition.
As Blackett also pointed out, at sufficiently high flows the capillary tube flow sensor response becomes a non-linear function of flow rate, responding now also to the cube of the flow rate and not just to the first power of flow. However, the cubic term depends in addition on the fluid thermal conductivity, and so at higher flows the simple gas conversion by gas heat capacity no longer holds, and the gas conversion becomes much more complicated. For this reason capillary tube mass flow meters and mass flow controllers are normally operated only in the linear response range of the capillary tube thermal flow sensor, where a constant gas correction factor independent of flow is sufficient for the conversion between flows of different known gases or mixtures of gases of known fixed proportions. The ISO standard for thermal flow meters cited above also describes features and use of capillary tube thermal flow meters and controllers operated in the linear portion of their flow response, including the routine use of gas correction factors for employing a meter calibrated on one gas to measure mass flow rates of other gases of known specific heat capacity, without requirement for recalibrating the instrument separately for each different gas or mixture of gases. The Sierra Instruments Inc. White Paper “Capillary Thermal Users Guide” provides a thorough summary of capillary tube thermal sensor flowmeters and controllers operated in the linear response of the flow sensor tube.
There is also a prior art patent for capillary tube thermal flow sensors teaching a method to allow operation with different gases even in the non-linear portion of the sensor flow response range, (Wang, Valentine, & Lull, U.S. Pat. No. 7,043,374, May 9, 2006). This patent may be summarized as follows.
It is asserted that for capillary tube sensors there exists a unique functional relationship between sensor output voltage, S, volume flow rate Q, sensor length L, conduit cross-sectional area A, fluid mass density ρ, fluid specific heat at constant pressure Cp and two empirically determined constants that are typically different for each fluid, f and g, such that
                              f          ·                      s            k                          =                  W          ⁡                      (                          g              ·                                                ρ                  ·                  Q                  ·                  L                                A                            ·                                                c                  p                                k                                      )                                              (        1        )            
Here W stands for a unique capillary sensor response function that is the same for all fluids and all sensors of a specific design. The assertion is that if the quantity on the left of equation (1) is considered to be a y coordinate, and the quantity in parenthesis on the right of Eq. (1) is considered to be an x coordinate, then a plot of y(x) based on measured sensor output S as a function of measured volume flow rate Q will give a unique nonlinear curve y(x) that is independent of gas or gas mixture species, despite the fact that S(Q) plotted vs. Q gives different curves for different gas and mixture species. To determine the flow of a gas of known composition from the relation of Equation (1), starting from the measured sensor voltage S, one must calculate the corresponding y from measured S and the two known gas properties f, k, then find from y the corresponding x coordinate on the previously determined unique curve y(x), and then use the known gas and dimensional sensor properties g, ρ, k, Cp, L and A to find the appropriate volume flow Q from the numerical value of the x coordinate of the curve. U.S. Pat. No. 7,043,374 discloses no specific analytical functional form or continuous curve for the function W; it apparently consists only of a set of associated discrete (x,y) points computed from the (S, Q) sensor output points resulting from calibration of the flow sensor on specific known gases. U.S. Pat. No. 7,043,374 also teaches no method for the determination of the empirical gas properties f,g required for each gas to apply the method. This omission is especially glaring in the case of process gases that are so reactive they cannot be safely used in production calibration, so that they are replaced by safer surrogate gases for manufacturing flow calibrations.
In summary, for prior art capillary tube thermal flow sensors operated in the linear portion of the sensor response there is a simple gas properties conversion that allows use of a sensor calibrated on one known gas to be used with many other known pure gases and gas mixtures of constant proportions provided the relative specific heat capacities of the gases or mixtures are all known. This property of capillary tube thermal flow sensors is well-known, and is described for instance in the ISO Standard issued Oct. 15, 2001 and titled “ISO-14511 Thermal Mass Flow Meters in Closed Conduits”.
For capillary tube sensors operated in the non-linear portion of the sensor response range the gas dependence is more complicated, and involves other gas properties besides fluid specific heat capacity. The prior art described in US patent by Wang, et al. U.S. Pat. No. 7,043,374 B2 teaches a method of operating such a capillary sensor in the non-linear part of the response curve providing one knows the density, thermal conductivity, and specific heat at constant pressure of each gas, plus the two empirically determined gas constants f and g for each gas, plus the length and cross-sectional area of the capillary tube sensor employed, and that one has previously measured the “characteristic curve” W using the sensor in question for all gases of interest with known properties. Because of the need to measure the new gas properties f and g for each gas of interest, this method is only practical for those with the resources needed to complete the necessary up-front flow testing, or who have access to a manufacturer's database containing this information.
In contrast, MEMS thermal flow sensors have a different dependence on gas properties than the capillary tube flow sensors, even in the linear response range where they have a dependence on fluid thermal conductivity and mass density as well as heat capacity. For example, those familiar with the capillary tube thermal flow meters know that in the linear flow response range of the sensor both hydrogen and air have nearly the same slope vs. standardized volume flow rate, so that the “gas correction factor” is close to 1 for these gases. However, for a MEMS thermal flow sensor with heating and sensing internal to the flow conduit the gases hydrogen and air have dramatically different slopes even in the linear region of the sensor response. Thus the same dimensionless correlation does not apply to both types of thermal flow sensor, and the correlation (1) taught in the prior art of U.S. Pat. No. 7,043,374 is not valid for MEMS thermal flow sensors with heater and temperature sensors directly exposed to the flowing fluid.
Therefore it has not previously been possible to use a MEMS thermal flow sensor with heater and temperature sensors immersed in the flowing fluid to measure flows with many gases based on a single flow calibration with only one gas, even in the linear response range, because no accurate and simple method of gas conversion was known. In addition, it has been the common practice with MEMS flow sensors to calibrate and use them over wide flow ranges where the response is highly non-linear for all gases or fluids used. Therefore it has heretofore been necessary to perform an expensive non-linear calibration with each gas or fluid that one wishes to use in a MEMS thermal flow meter, with the result that the high cost of multiple non-linear calibrations has largely restricted use of the MEMs-based flow meters to flows of the most common gas mixture, air.